2.1 Introduction

Screen Readable NCERT Class 12 Mathematics Textbook for Blind and Visually Impaired Students Prepared by Dr T K Bansal.

In Chapter 1, we have studied that the inverse of a function f, denoted by f^−1, exists if f is one-one and onto. There are many functions which are not one-one, onto or both and hence we cannot talk of their inverses. In Class 11, we studied that trigonometric functions are not one-one and onto over their natural domains and ranges and hence their inverses do not exist. In this chapter, we shall study about the restrictions imposed on domains and ranges of trigonometric functions which ensure the existence of their inverses and observe their behaviour through graphical representations. Besides, some elementary properties will also be discussed.

The inverse trigonometric functions play an important role in calculus, for they serve to define many integrals. The concepts of inverse trigonometric functions is also used in science and engineering.